U.S. patent number 6,982,669 [Application Number 10/488,941] was granted by the patent office on 2006-01-03 for hybrid inertial navigation system with improved integrity.
This patent grant is currently assigned to Thales. Invention is credited to Jacques Coatantiec, Patrice Guillard.
United States Patent |
6,982,669 |
Coatantiec , et al. |
January 3, 2006 |
Hybrid inertial navigation system with improved integrity
Abstract
The invention relates to an internal platform hybridized with a
GPS receiver. The hybridization is achieved through a Kalman filter
through which a new hybrid position D-HYB is estimated on the basis
of a noted deviation between pseudo-distance measure by the
receiver between the receiver and the various satellites and
corresponding distances computed by the inertial platform between
the platform and the same satellites. In this filtering, the
distance increment from one measurement instant to the next
instant, between the pseudo-distance previously measured by the
receiver on a satellite axis of a deviation and the new
pseudo-distance measured by the receiver on a satellite axis of a
deviation and the new pseudo-distance measured by the receiver on
this axis, is the phase variation .DELTA..PHI.=.PHI.(t)-.PHI.I
(t-1) of a digital oscillator between the two measurement instants,
this variation being referred to distance along the satellite axis.
The oscillator is that which makes it possible to slave the local
carrier frequency in the receiver to the carrier frequency received
from the satellite. Application to the measurement of position.
Inventors: |
Coatantiec; Jacques (Bourg les
Valence, FR), Guillard; Patrice (Valence,
FR) |
Assignee: |
Thales (Neuilly sur Seine,
FR)
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Family
ID: |
8867747 |
Appl.
No.: |
10/488,941 |
Filed: |
September 24, 2002 |
PCT
Filed: |
September 24, 2002 |
PCT No.: |
PCT/FR02/03258 |
371(c)(1),(2),(4) Date: |
March 09, 2004 |
PCT
Pub. No.: |
WO03/029755 |
PCT
Pub. Date: |
April 10, 2003 |
Prior Publication Data
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Document
Identifier |
Publication Date |
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US 20040239560 A1 |
Dec 2, 2004 |
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Foreign Application Priority Data
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Sep 28, 2001 [FR] |
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01 12546 |
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Current U.S.
Class: |
342/357.62;
701/469 |
Current CPC
Class: |
G01C
21/165 (20130101); G01S 19/20 (20130101); G01S
19/47 (20130101) |
Current International
Class: |
H04B
7/185 (20060101) |
Field of
Search: |
;342/357.01,357.06,357.14 ;701/207,213,216,220 |
References Cited
[Referenced By]
U.S. Patent Documents
Foreign Patent Documents
Primary Examiner: Phan; Dao
Attorney, Agent or Firm: Lowe Hauptman & Berner, LLP
Claims
What is claimed is:
1. A navigation system, comprising: an inertial navigation platform
hybridized with at least one satellite based positioning receiver,
the inertial platform providing position information resulting at
least in part from accelerometric and gyrometric measurements, and
the receiver providing pseudo-distances representing the distance
between the receiver and satellites, the receiver comprising, for
each channel of the receiver, a digitally phase controlled
oscillator slaved to the phase of a carrier of a satellite signal
corresponding to this channel; wherein the navigation system
provides hybrid position values resulting from a combination of
numerical position data originating from the platform and numerical
data originating from the receiver; a means of estimating a new
hybrid position on the basis of an observed deviation between
pseudo-distances measured by the receiver between the receiver and
each one of said satellites and corresponding distances computed by
the inertial platform between the platform and said each one of
said satellites, this means comprising a digital filter, of Kalman
filter type, allowing the prediction of a deviation and the
matching of the filter as a function of the comparison between the
observed deviations and predicted deviations; wherein in the
digital filter, the distance increment from one measurement instant
to the next instant, between a pseudo-distance previously measured
by the receiver on a satellite axis and a new pseudo-distance
measured by the receiver on said satellite axis, is the phase
variation of the digital oscillator between the two measurement
instants, this variation being referred to distance along said
satellite axis.
2. The navigation system as claimed in claim 1, wherein the
estimating means also provides a protection radius associated with
the hybrid position found, this protection radius being calculated
on the basis of variance data produced in the Kalman filter thus
incremented.
3. A method of estimating position using a navigation system having
an inertial navigation platform hybridized with at least one
satellite based positioning receiver, the inertial platform
providing position information resulting at least in part from
accelerometric and gyrometric measurements, comprising the steps of
providing pseudo-distances representing the distance between the
receiver and satellites; the receiver comprising, for each channel
of the receiver, a digitally phase controlled oscillator slaved to
the phase of a carrier of a satellite signal corresponding to this
channel; providing hybrid position values resulting from a
combination of numerical position data originating from the
platform and numerical data originating from the receiver;
estimating a new hybrid position on the basis of an observed
deviation between a pseudo-distances measured by the receiver
between the receiver and each one of said satellites and a
corresponding distances computed by the inertial platform between
the platform and said each one of said satellites, predicting a
deviation and the matching of the filter as a function of the
comparison between the observed deviations and predicted
deviations; calculating a distance increment which is a phase
variation of said digital oscillator between one measurement
instant and a next measurement instant, this variation being
referred to distance along a satellite axis, and adding this
increment to a pseudo-distance measured by the receiver on a
satellite axis at said one measurement instant to obtain a new
pseudo-distance on said satellite axis, and using said new
pseudo-distance to compute said observed deviation at said next
measurement instant.
4. The method as claimed in claim 3, providing a protection radius
associated with the hybrid position found, this protection radius
being calculated on the basis of variance data produced in the
Kalman filter thus incremented.
Description
CROSS-REFERENCE TO RELATED APPLICATIONS
The present Application is based on International Application No.
PCT/FR02/03258, filed on Sep. 24, 2002, which in turn corresponds
to FR 01/12546 filed on Sep. 28, 2001, and priority is hereby
claimed under 35 USC .sctn.119 based on these applications. Each of
these applications are hereby incorporated by reference in their
entirety into the present application.
FIELD OF THE INVENTION
The invention relates to instruments for aiding navigation and
piloting, and in particular to those which are intended for aerial
navigation in which the constraints regarding accuracy in position
and speed are high and in which the integrity of the information
given by the position and speed measuring instruments must be
ascertained at every moment.
The use of inertial navigation platforms in aircraft is very
conventional today. These platforms use accelerometers to determine
accelerations along axes defined with respect to the aircraft,
gyrometers to determine angular speeds of rotation with respect to
axes likewise defined with respect to the aircraft, and possibly
other sensors such as a baro-altimeter. By integrating the
gyrometric measurements, one determines the orientation of the
aircraft at a given moment; by integrating the accelerometric
measurements, which may be referred to a terrestrial reference
frame outside the aircraft by virtue of the knowledge of the
orientation of the aircraft, one determines the aircraft's velocity
components in this terrestrial reference frame. By integrating the
velocities, one determines geographical positions.
BACKGROUND OF THE INVENTION
Measurement sensors are however imperfect and exhibit intrinsic
errors or measurement bias, which may moreover vary during
navigation. Furthermore, they are subject to measurement noise, in
the sense that random variations not corresponding to the
variations in the measured quantity get superimposed on the useful
signal, representing the physical quantity sought. The electrical
measurement signals are furthermore processed by electronic
circuits which themselves introduce noise.
The bias and measurement noise are all the more detrimental since
the position computations made on the basis of the measurement
results from the sensors involve integrations. The integration
gives rise to a drift in the measured value, which drift increases
progressively over time when the integrated value is biased at the
start. Double integration (integral of acceleration to give the
speed followed by integral of speed to give the position) further
increases this drift in considerable proportions.
To summarize, inertial platforms are very accurate over a very
short duration but are subject, owing to the systematic time
integration of the biases, to a sizeable drift which makes it
necessary to reset them periodically on the basis of other position
information (or speed information).
A mode of resetting that has long been used has consisted in using
a network of ground beacons to provide aircraft overflying them
with position signals making it possible to reset their navigation
instruments.
More recently, inertial platforms have begun to be reset on the
basis of satellite based positioning receivers carried onboard
aircraft and deriving position and speed information, in a
terrestrial reference frame, from signals that they receive from
the satellites.
Hybrid platforms are thus produced that profit both from the
excellent very short term measurement quality of inertial platforms
(measurement hardly affected by noise) and from the high geographic
position accuracy offered by satellite based positioning
systems.
However, the position measurements made by satellite based
positioning receivers are intrinsically greatly affected by noise
in the short term, so that their measurements would have to be
averaged in order to determine an accurate position; however, in a
mobile vehicle, and especially an airplane moving rapidly, it is
not possible to wait to average the measurements in order to obtain
an accurate position since the airplane will have moved between two
measurements.
Other problems may arise, such as changes of constellation of
satellites observed by the receivers, that give rise to abrupt
jumps in measured position, or faults with satellites that emit
erroneous signals, or even faults with the inertial platform.
SUMMARY OF THE INVENTION
The hybridization of the two systems, inertial system and satellite
based positioning system, to improve the quality of the position
and speed measurements, poses difficult problems.
In general, one tries to best solve these problems through the use
of filtering algorithms, generally known by the name Kalman
filterings. This is a digital filtering performed during the
computations that make it possible to determine a position known as
the "hybrid position" on the basis of the information originating
from the inertial platform and information given by the satellite
based positioning receiver.
In case of loss or of degradation of the satellite based
positioning measurements (in respect of which it should be recalled
that they may easily be lost because the signal emitted by the
satellites is extremely weak and that they may be erroneous, for
example on account of the presence of multipaths between a
satellite and the receiver), the Kalman filtering makes it possible
to continue to compute a hybrid position which is of inertial type
(that is to say analogous to one that would be provided by an
inertial platform entirely on its own) but which is corrected of
the platform's drift errors; specifically, the Kalman filter
computes these errors continuously and can make use of the errors
referenced just before the loss of the satellite signals to
continue to correct the platform after this loss up to the moment
at which the satellite signals become reavailable.
However, the accuracy and reliability of hybrid inertial platforms
corrected by satellite based positioning receivers is not
sufficient for certain applications, such as the automatic landing
of aircraft. More generally, one wishes to constantly improve the
accuracy of the measurements of position, of speed, of attitude,
etc., of the vehicles, and it is moreover often necessary not only
to give a position with accuracy, but also to ascertain the value
of the accuracy associated with a measurement, given that this
value is not fixed (it depends on a great number of parameters) and
that it may be useful for enabling decisions to be taken. For
example, in case of descent below a certain accuracy threshold, the
aircraft's onboard computer can trigger an alarm intended to
prohibit the carrying out of a landing.
One seeks in particular to be capable of giving a position with
accuracy even if one of the satellites exhibits a defect such as a
small clock drift. A satellite clock drift is a defect which is
particularly difficult to detect through a satellite based
positioning receiver and even through an inertial/satellite hybrid
platform; specifically, the signals emitted by the satellite
continue to exhibit all the appearances of intact signals. However
they are erroneous, and the absence of any jump of position in the
results provided periodically by the satellite based signals
receiver implies that the fault is very difficult to detect.
Nevertheless, it is necessary that the user or the onboard computer
be alerted to this type of defect.
An aim of the present invention is therefore to improve hybrid
inertial navigation platforms using satellite based positioning
receivers, and most particularly those which provide not only a
hybrid position but also a radius of protection around this
position, inside which radius the integrity of the position is
guaranteed with an error probability which is bounded by a defined
upper value. This concept of radius of protection will be returned
to in greater detail.
According to the invention, use is made of a Kalman filter (that is
to say a filter employing prediction and resetting of estimation
error, based on a model of temporal propagation of the errors of
the system to be corrected and on a comparison with observed
measurement values), whose particular feature is as follows: it
uses as observed measurement values, to be compared periodically
with predicted values, the differences between on the one hand the
pseudo-distances measured by the receiver of satellite signals
between this receiver and the various satellites and on the other
hand the corresponding distances calculated by the inertial
platform between the platform and the same satellites, the distance
increment from one measurement to the next between the
pseudo-distance previously measured by the receiver and the new
pseudo-distance measured on a satellite axis being determined by a
counting of the phase variation of the carrier frequency of the
satellite signals from the previous measurement and not by an
independent pseudo-distance measurement.
To do this, the filtering employing prediction and resetting of
error uses, for each satellite axis, an initial position of the
receiver, relative to the satellite, which is a position obtained
by calculation on the basis of the temporal positions of
pseudo-random codes present in the signals received from the
satellites and it stores the phase of the carrier at the moment of
this position measurement; and moreover, it uses, as new position
of the receiver with respect to the satellite, during the next step
of observation of the position of the receiver, not a new position
measurement, but a simple modification of the previous position, by
addition of the phase variation, in terms of number of phase
revolutions and fraction of a revolution, referred to distance
along the satellite axis, of the carrier frequency of the satellite
signal.
Stated otherwise, the Kalman filters that could be proposed in the
past, for inertial hybrid platforms reset by satellite positioning,
generally use as observed position measurement, for resetting the
inertial errors propagation model, a position variation in
geographical axes, or a variation of pseudo-distances along the
satellite axes, the variation of pseudo-distance resulting from the
variations of temporal position of the local pseudo-random code of
a channel of the positioning receiver. Here, the position increment
between two resettings does not result from this variation of
temporal position of the pseudo-random code, it results from the
variation of phase of the carrier on each satellite/receiver
axis.
It is recalled that a conventional satellite based positioning
receiver comprises a feedback control of a local pseudo-random code
for each channel corresponding to a satellite, and a feedback
control of the phase of the carrier frequency of the satellite
signal. This second feedback control, coupled with the first,
serves in particular to take into account the Doppler effect
induced by the relative speed of the receiver with respect to a
satellite along the axis connecting the receiver to the satellite.
The code feedback control uses a first digitally controlled
oscillator to establish and synchronize the local code which allows
the pseudo-distance determination, while the carrier feedback
control uses a second digitally controlled oscillator which makes
it possible to establish a local phase variation slaved to the
phase of the carrier. These oscillators deliver a numerical phase
value that increases by increments controlled by a computer which
oversees the digital feedback control circuits. According to the
invention, to observe the variations in distance between the
receiver and a satellite with the aim of resetting an inertial
platform through a satellite based positioning receiver, use is
made of the digital output of the second digitally controlled
oscillator and the variation in phase observed on the second
oscillator, and referred to a distance of propagation of the
satellite signal (whose frequency is known), is added to the
distance previously calculated by the receiver.
Consequently, the invention proposes a navigation system comprising
an inertial navigation platform hybridized with at least one
satellite based positioning receiver, the inertial platform
providing position information resulting at least in part from
accelerometric and gyrometric measurements, and the receiver
providing pseudo-distances representing the distance between the
receiver and satellites, the receiver comprising, for each channel
of the receiver, a digitally phase controlled oscillator slaved to
the phase of a carrier of a satellite signal corresponding to this
channel, and the navigation system providing hybrid position values
resulting from a combination of numerical position data originating
from the platform and numerical data originating from the receiver,
the system comprising a means of estimating a new hybrid position
on the basis of a noted deviation between on the one hand
pseudo-distances measured by the receiver between the receiver and
the various satellites and on the other hand corresponding
distances computed by the inertial platform between the platform
and the same satellites, this means comprising a digital filter, of
Kalman filter type, allowing the prediction of a deviation and the
matching of the filter as a function of the comparison between the
noted deviations and predicted deviations, characterized in that,
in the digital filter, the distance increment from one measurement
instant to the next instant, between the pseudo-distance previously
measured by the receiver on a satellite axis with a view to the
noting of a deviation and the new pseudo-distance measured by the
receiver on this axis, is the phase variation of the digital
oscillator between the two measurement instants, this variation
being referred to distance along the satellite axis.
The resetting of the inertial platform is therefore done by
regularly observing the alterations in the phase of the carrier on
each channel of the receiver, these alterations having the
characteristic of hardly being affected by noise, and this will
make it possible not only to obtain an accurate hybrid position but
also to obtain an effective measurement of the accuracy of
determination of the hybrid position, in the form of a calculation
of a protection radius. The calculation of the protection radius is
done according to the invention on the basis of the same Kalman
filter, incremented in the manner indicated above.
The initial setting of the hybrid system is done in principle by
giving the hybrid position an initial value which is a position
calculated by the satellite based positioning receiver on the basis
of the temporal position of the pseudo-random codes present in the
signals from the various satellites.
A direct resetting (reinitialization of the inertial platform) by a
new determination of a satellite position may be done when the
actual radius of protection of the satellite based positioning
receiver (which provides pseudo-distances with a certain protection
radius depending in particular on the configuration of the
currently observed constellation of satellites) becomes smaller
than the radius of protection of the hybrid platform. This is why
it is particularly advantageous to calculate both an actual radius
of protection of the measurements provided by the receiver and a
radius of protection of the measurements provided by the hybridized
platform.
BRIEF DESCRIPTION OF THE DRAWINGS
Other characteristics and advantages of the invention will become
apparent on reading the detailed description which follows and
which is given with reference to the appended drawings in
which:
FIG. 1 diagrammatically represents the principle of a hybrid
inertial platform according to the invention;
FIG. 2 represents a flowchart of the operation of the Kalman
filter;
FIG. 3 represents the general structure of a satellite based
positioning receiver, comprising a digitally controlled oscillator
whose output represents the phase of the carrier of the satellite
signal;
FIG. 4 represents the general architecture of the calculations of
radii of protection.
DETAILED DESCRIPTION OF THE INVENTION
The hybridized inertial platform comprises an inertial platform
proper C.sub.--INERT, a satellite based positioning receiver, that
will be referred to subsequently as the GPS receiver with reference
to the most common positioning system known as "Global Positioning
System", and a hybridization electronic computer
CALC.sub.--HYB.
The inertial platform C.sub.--INERT is usually composed of several
accelerometers, typically three, with fixed orientations with
respect to the aircraft, providing values of acceleration along
these axes; several gyrometers, typically three, each having a
fixed axis with respect to the airplane and providing values of
speed of angular rotation about these axes, a computer which
determines digital data relating to geographical position (Lat,
Lon, Alt), geographical speed (Vn, Ve, Vv), heading roll and pitch
attitudes (.phi., .theta., .psi.), etc., on the basis of the
indications provided by the accelerometers and gyrometers; the
computer also provides a temporal marking pulse defining the
instant at which these data are valid.
All these data, referred to hereinafter as raw inertial data
D-INERT, are provided by the inertial platform to the hybridization
computer.
Possibly, other sensors may be associated with the platform so as
to refine the computations, such as a barometric altimeter
(ALT-BARO). The computer of the inertial platform then uses the
information from this or these additional sensors at the same time
as the information from the gyrometers and accelerometers.
The GPS receiver conventionally provides a geographical position in
terms of longitude, latitude and altitude, also referred to as the
resolved position, also including a position measurement time. The
receiver in principle also provides speeds of displacement with
respect to the earth. The set consisting of this position, this
time and this speed is referred to as the PVT point. A temporal
marking pulse defining the instant of validity of the PVT point is
also provided.
For its operation, the GPS receiver uses a measurement of distances
between the receiver and each satellite in sight of the receiver.
These distances are in reality pseudo-distances PD.sub.i (i
designating a satellite number) obtained in the form of durations
of signal propagation between the satellite of rank i and the
receiver along the axis (satellite axis) joining the satellite and
the receiver. It is the combination of the pseudo-distances on
several satellite axes together with the knowledge of the positions
of the satellites at a given moment (which knowledge is sent in the
form of ephemerides by the satellites themselves) that makes it
possible to compute the PVT resolved position.
The pseudo-distances PD.sub.i are therefore available in the GPS
receiver and they will be used for the hybridization between the
inertial platform and the GPS receiver. The resolved position
information could naturally be used to carry out the hybridization
by comparing the GPS resolved position with the position computed
by integration in the inertial platform, but, as will be seen
later, the use of pseudo-distances makes it possible to carry out
the hybridization while taking account of possible faults or
defects present in the signal emanating from a satellite.
The GPS receiver establishes other data too, and in particular the
ephemerides representing the position of the satellites at any
instant, a signal/noise ratio (S/N).sub.i for each satellite, and
one or more values of protection radius Rp1 (in terms of horizontal
distance), Rp2 (in terms of vertical distance) which represent a
measurement accuracy and to which we shall return later.
The GPS receiver provides the hybridization computer CALC.sub.--HYB
with all these data, referred to hereinafter as D.sub.--GPS (GPS
data).
The raw inertial data D.sub.--INERT and the GPS data are processed
in the hybridization computer so as to provide hybrid inertial data
D.sub.--HYB which are a hybrid attitude, a hybrid speed and a
hybrid position. The hybridization computer also provides one or
more values of protection radius RPH representing the accuracy of
the data emanating from the hybridization. Finally, the computer
can provide data for identifying an errant satellite and naturally
may provide alarm signals when the computation of the radii of
protection demonstrates insufficient reliability of the information
provided.
For the implementation of the invention, the GPS receiver also
provides the hybridization computer with an indication, for each
satellite observed, of the phase .PHI..sub.i of the carrier of the
satellite signal of rank i at the instant of observation.
The hybridization is achieved through Kalman filtering algorithms
so as to obtain at one and the same time the qualities of stability
and of absence of short-term noise of the inertial platform and the
very high accuracy of the GPS receiver, although greatly affected
by short-term noise. The Kalman filtering makes it possible to take
account of the intrinsic errors of behavior of the inertial
platform C.sub.--INERT, and to correct these errors. The
measurement error of the inertial platform is determined during
filtering; it is added to the measurement provided by the platform
so as to give a hybrid measurement in which the errors due to the
behavior of the platform are minimized.
Moreover, the implementation of a filtering algorithm, using the
pseudo-distances emanating from the GPS receiver and the phases of
the carrier of the satellite signals, is such that it is possible
to determine the errant satellites, exclude them, and compute the
radii of protection of the hybrid position both in the absence of
satellite defect and in the presence of a defect.
The hybridization computer is therefore designed both to correct
the errors inherent in the inertial platform and to take account of
the defects of the spatial segment of the reception of the
satellite signals.
It is also possible to envisage additional means for detecting (but
not necessarily correcting) hardware defects of the inertial
platform (unmodeled defects, that is to say faults) and hardware
defects of the GPS receiver. These means consist in practice in
envisaging redundant chains, with another inertial platform,
another GPS receiver and another hybridization computer. This type
of redundancy does not form the subject of the present invention
and will not be described, but the invention may be incorporated in
redundant systems as in nonredundant systems.
The hybridization is done in open loop, that is to say the inertial
platform is not slaved to the data resulting from the
hybridization.
In a general manner, it is necessary to introduce initial values
into the inertial platform and into the hybridization computer.
These initial values are given the first time with reference to an
absolute reference frame: for example on departure of an airplane
on the ground, motionless, in a known attitude and at a known
position, this attitude and this position are introduced as initial
values into the filter. Subsequently, during flight, the
measurements provided by the inertial platform will be
reinitialized from time to time as a function of the measurements
provided by the GPS receiver.
The manner in which the Kalman filtering is implemented in order to
combine information emanating from the inertial platform and
information from the GPS receiver will now be described.
FIG. 2 represents a flowchart of the operation of this filtering
(which is an algorithmic filtering implemented on digital data).
The filtering which is described assumes that there are N
satellites observed by the GPS receiver. As will be seen later,
there will in fact be N+1 different Kalman filterings: on the one
hand a main filtering, based on the measurements emanating from the
N satellites, and leading to the correction of the measurements of
the inertial platform, and N secondary filterings, each based on
the reception of N-1 satellites only. Each secondary filtering
corresponds to the exclusion of one and only one satellite, and the
comparison of the results of the N secondary filterings and of the
main filtering allows one to possibly reach the conclusion that a
satellite is defective and even to the decision to exclude this
satellite for the measurements which follow. The main filtering and
the N secondary filterings are defined by N+1 computation programs
operating either in parallel with N+1 processors, or under time
sharing with a single processor or a reduced number of
processors.
Given that the secondary filterings operate on the same principles
as the main filtering, the only difference pertaining to the number
of satellites observed, it is sufficient to describe the operation
of the main filtering.
The principle of Kalman filtering is recalled:
The various causes of drift or of errors of the inertial platform
C.sub.--INERT are known and may be modeled. The Kalman filtering
consists in establishing, on the basis of this knowledge of the
behavior of the platform in the presence of various causes of
error, a state vector X representing the errors estimated in the
various information components emanating from the inertial
platform, and a matrix F representing the coefficients of
propagation of these errors over time.
The error propagation model is expressed in the form of a law of
propagation of the inertial errors, of the form X'=F.X where X' is
the time derivative of the vector X. The error in a data item
depends on the errors in the other data items, hence the matrix
form of the propagation law.
The matrix F is a matrix of coefficients which are not necessarily
constant and which may vary for example as a function of the output
values of the hybrid inertial platform. The filter comprises the
means of computation and of updating of the various terms of the
matrix.
Moreover, the model of the behavior of the inertial platform is
also defined by a covariance matrix (matrix P). The coefficients of
this matrix represent the variance of each of the components of the
state vector and the covariance of the various pairs of components
of this vector. The matrix P represents as it were the degree of
confidence allocated to the updated state vector. The covariance
matrix P itself varies over time, the temporal propagation law for
this matrix being of the form: P'=F.P.F.sup.T+Q,
Where P' is the time derivative of the matrix P; F.sup.T is the
transpose of F; and Q is a variance matrix of a noise vector W
having a noise component for each data item of the state vector X.
This vector W is a white noise vector making it possible to
quantify the approximations made in the modeling for each component
of the state vector X.
Finally, for the hybridization proper, a predicted vector Yp is
established, this being a linear combination Yp=H.Xp of a
prediction Xp of the state vector X (the coefficients of the linear
combination varying over time); and the components of the predicted
vector Yp are compared with similar components of a vector Yo
observed with the aid of the GPS receiver and of the inertial
platform. The term H is a matrix representing the coefficients of
the linear combination; to elucidate the nature of this matrix, the
following thing may be said: if the GPS receiver provides
pseudo-distances observed between the receiver and a satellite,
hence along satellite axes, and if one wishes to make use of these
observed pseudo-distances to reset the hybrid position, then the
Kalman filter must comprise computation means for establishing
predicted "pseudo-distances" along the satellite axes, before
detecting a deviation between the predicted pseudo-distances and
the pseudo-distances observed along the same axes. It is the role
of the matrix H to convert certain components of the state vector X
(which a prior are not distances along the receiver/satellite axes)
into distances along the receiver/satellite axes.
In the Kalman filter that will be used in practice, the components
of the state vector X are the deviations between reality and the
data provided by the inertial platform before hybridization. Stated
otherwise, if .phi., .theta., .psi., Lat, Lon, Alt, are six
attitude and position data items provided by the inertial platform
C.sub.--INERT (there are in practice still other data provided by
the inertial platform), the state vector X consists of a column of
components .delta..phi., .delta..theta., .delta..psi., .delta.Lat,
.delta.Lat, .delta.Alt, etc., representing the deviations between
the exact values and the values actually provided by the inertial
platform C.sub.--INERT.
The Kalman filter operates globally on the following general
principle: on the basis of a current value of the state vector X
and of the covariance matrix P of the state vector, the model for
the propagation of the inertial errors (matrix F, differential
equations of propagation) establishes a predicted state vector Xp;
this vector is transformed into a predicted observable vector Yp;
the GPS receiver and the inertial platform provide data that make
it possible to compute an observed vector Yo; the predicted
observable vector Yp and the observed vector Yo are compared; the
difference, multiplied by a gain matrix K computed from the matrix
P, serves to compute a new estimate Xa of the state vector X and a
new estimate of the matrix P; this estimate Xa will be substituted
for the previous value of the state vector so as to become a new
current value of the state vector; this substitution is the
operation of resetting the model, performed periodically; likewise,
an estimate Pa of the matrix P will be substituted for the previous
value. Finally, with the new value of the state vector, the data
D.sub.--INERT provided by the inertial platform are corrected to
produce corrected data or hybrid data D.sub.--HYB at the output of
the hybridized platform. The correction at this juncture is a
simple addition between the raw data D.sub.--INERT provided by the
inertial platform and the state vector Xa which represents the
current estimate of the errors produced by the inertial
platform.
The values observed (vector Yo) by the hybridized inertial
platform, which are established with a view to comparison with
values Yp predicted by the Kalman filter, are then deviations
between data provided by the GPS receiver and comparable data
provided by the inertial platform. These deviations are, as far as
the position measurements are concerned, distances along the axes
connecting the platform to the satellites.
This is represented by the operating flowchart of FIG. 2. The
details of the manner of operation will now be described.
The model for the propagation of the inertial errors is represented
by the matrix F, the matrix P, the matrix Q, the state vector X,
and the differential equations X'=F.X and P'=F.P.F.sup.T+Q.
The matrix F has fixed coefficients and others which depend on the
position at which the platform is located; these latter
coefficients are therefore periodically updated as a function of
the hybrid data D.sub.--HYB emanating from the hybridized platform,
that is to say resulting ultimately from the computations done by
the hybridization computer.
On departure, the state vector X is initialized to zero. The hybrid
output data D.sub.--HYB are preferably initialized to values
provided either by the GPS receiver, or by known data (airplane
motionless on the ground, of which both the geographical position
and the attitude are known).
The matrix P is initialized with the variances and covariances
known at the place where the initialization is done, in particular
those related to the GPS receiver.
The differential equations of the model thus initialized involve
the matrix F, the matrix P and the matrix Q; they make it possible
to determine a predicted vector Xp from the current vector X, and a
predicted covariance matrix Pp from the current matrix P.
Of interest chiefly in what follows are the position components of
the state vector, and hence only these components will be
mentioned, given that the position is the most important element
which justifies the hybridization between the inertial platform and
the GPS receiver. Naturally, the reasoning is the same for the
velocity components, and for other components of the state
vector.
On the basis of the predicted vector Xp, converted into satellite
axes by the matrix H, a predicted observable vector Yp=H.Xp is
computed. The matrix H is computed on the one hand from the
ephemerides of the satellites, making it possible to determine the
position of the satellites at a given instant, and on the other
hand from the inertial position given by the inertial platform
C.sub.--INERT. The predicted vector Yp corresponds to predicted
errors, referred to satellite axes.
The predicted errors Yp are compared with the errors actually
observed Yo. The errors observed comprise position components
Yo.sub.i, on each satellite axis; these components consist of a
difference between the receiver-satellite distance PD.sub.i as
measured by the GPS receiver and the inertial platform/satellite
distance PC.sub.i computed from the inertial position given by the
platform C.sub.--INERT and the ephemerides detected by the GPS
receiver. Yo.sub.i=PC.sub.i=PD.sub.i
The difference, at each resetting operation, between the predicted
vector Yp and the observed vector Yo, is the vector quantity
serving for the reset. This difference is called the innovations
vector: INNOV=Yo-Yp=Yo-H.Xp
It represents the fact that the prediction is not perfect since Yp
was predicted and Yo is observed, and that the state vector Xp and
the predicted matrix Pp must be modified so as to get closer to a
state vector X and a matrix P which properly model the actual
behavior of the inertial platform.
The innovations (components of the vector INNOV) are not applied in
an abrupt manner to the predicted state vector Xp to construct a
new current vector X. On the contrary, only a fraction of the
innovations (fraction less than 1) is applied to the predicted
vector to construct an updated vector, and it is only gradually,
progressively with the gradual resets, that the predicted vector
will get closer to the observed vector Yo.
A gain matrix K is therefore calculated so as to determine, for
each component of the state vector, a respective gain less than 1,
representing the fraction of innovation that will be added to the
predicted component to define an updated component of the state
vector.
The equation for updating the state vector from X to Xa is then:
Xa=Xp+K.(Yo-Yp)
The matrix K is calculated by taking account of the matrix H, so as
to reconvert into the reference frame of the state vector X the
innovations Yo-Yp which are in satellite axes. Furthermore, the
gain matrix is computed from the predicted variance matrix Pp, the
gain allocated to the innovations so as to converge to the best
possible hybrid solution being dependent on the confidence that one
has in the exactness of the state vector.
The computation of the matrix K is done through the equation:
K=P.H.sup.T[H.P.H.sup.T+R].sup.-1
R is a matrix of noise components representing the inherent noise
of the GPS receiver when this noise can be measured by the GPS
receiver. For this purpose, a signal/noise ratio (S/N).sub.i data
item is preferably provided by the GPS receiver for each satellite.
The noise is easily measured by a correlator not aligned with the
pseudo-random code which modulates the satellite signal, this
correlator receiving the satellite signals and other signals
present in the same frequency band, the whole representing the
noise.
The computation of the gain matrix K is redone at each resetting
operation, the gains in the innovations along the axes of the state
vector varying over time not only due to changes in the covariance
matrix, but also due to changes in the orientation of the satellite
axes.
The updated state vector Xa will replace the previous state vector
X upstream of the model for the propagation of the inertial errors,
for the computation of a new error prediction and so on and so
forth.
In parallel with the computation of an updated state vector, an
updated covariance matrix Pa is computed from the predicted
covariance matrix Pp. The computation of the updated matrix Pa
results from the formula: Pa=Pp-K.H.Pp
The updated matrix Pa will replace the covariance matrix P at the
input of the inertial error propagation model, with a view to a new
prediction and a new resetting.
It is on the basis of the updated state vector Xa, which is a
vector estimating the errors of the inertial platform, that the
hybrid solution is computed: the components of the hybrid solution
(position, attitudes, speeds, etc.) are obtained by adding to the
corresponding components provided by the inertial platform (raw
inertial data) the updated estimate Xa of the errors due to the
inertial platform: D.sub.--HYB=D.sub.--INERT+Xa
In parallel, it is on the basis of the updated covariance matrix Pa
that it is possible to compute a radius of protection of the hybrid
measurements: the matrix Pa makes it possible to compute a radius
of protection of the hybrid measurement directly on condition that
there is no fault. This computation of protection radius will be
made explicit later.
However, as stated, if in addition to the main Kalman filtering
algorithm just described, one also envisages N secondary algorithms
excluding a satellite axis on each occasion, this is to also allow
determination of an errant satellite, the exclusion of this errant
satellite, and the determination of an associated protection radius
in the presence of a fault. These matters relating to radii of
protection will be returned to later.
For this Kalman filtering algorithm, both the main algorithm and
the secondary algorithms, it is envisaged that the differences
Yo.sub.i=PC.sub.i-PD.sub.i be computed, these being, on each
nonexcluded satellite axis of rank i, the difference between the
receiver/satellite distance measured by the inertial platform and
the same distance measured by the GPS receiver.
According to the invention, for this computation of the observed
measurement quantity Yo, the distance measured by the GPS receiver
on satellite axis i is obtained, from one reset operation to the
next, by adding to the distance previously observed a distance
corresponding to the carrier phase variation of the satellite
signal between the current reset operation and the previous reset
operation.
PD.sub.i(t)=PD.sub.i(t-1)+.lamda...DELTA..PHI..sub.i/2.pi. where t
is the time (counted in units corresponding to the duration
separating two successive resets, for example one second);
PD.sub.i(t) represents the distance computed at the moment of the
current reset, PD.sub.i(t-1) therefore represents the distance
computed upon the previous reset; .DELTA..PHI..sub.i is the carrier
phase variation observed between t-1 and t; .lamda. is the
wavelength (known) of the carrier of the satellite signal;
.lamda...DELTA..PHI..sub.i/2.pi. is the length, along the satellite
axis of rank i, corresponding to the distance of propagation of the
satellite signal for a phase variation .DELTA..PHI..sub.i.
Upon initialization of the system, the distance PD.sub.i(0) is the
pseudo-distance measured by the satellite based positioning
receiver, but, at the same time as this distance is computed, the
value of the carrier phase .PHI..sub.i(0) at the instant of
validity of the measurement is held in memory. Likewise, at each
reset step, the value of the carrier phase .PHI..sub.i(t-1) is kept
in memory with a view to the next step. During subsequent resetting
steps, the phase variation is computed by simple differencing
between the value .PHI..sub.i(t) of the current carrier phase and
the previous value .PHI..sub.i(t-1).
.DELTA..PHI..sub.i=.PHI..sub.i(t)-.PHI..sub.i(t-1)
And it is this variation, multiplied by .lamda./2.pi. to reduce it
to a propagation distance, which is added to the pseudo-distance
previously computed to define the new pseudo-distance serving for
the computation of the observed quantity Yo.sub.i.
The phase .PHI..sub.i(t) is obtained on the basis of the content of
a digitally controlled oscillator present in the feedback control
circuit for slaving the carrier phase of each channel (there is one
channel per satellite) of the GPS receiver.
FIG. 3 represents an exemplary structure of a digital channel of a
GPS receiver comprising such a phase feedback control circuit. All
the GPS receivers currently comprise in each channel such a carrier
phase feedback control circuit, and this circuit always comprises a
digitally controlled oscillator to establish a sawtooth linearly
varying phase representing at a given instant, due to the feedback
control, the phase of the carrier of the satellite signal.
The radio signal S.sub.--gps emanating from the satellites and
frequency transposed, is for example sampled by an analog/digital
converter ADC, which provides periodic samples, in phase (Ibb) and
in phase quadrature (Qbb). These samples are multiplied
(multipliers 12, 14, 16, 18) by a pseudo-random code corresponding
to the channel considered and hence to the satellite considered.
Two different correlations may be performed simultaneously, one
with a punctual code P (multipliers 12, 14) and the other with an
early-late code E-L (multipliers 16, 18). The pseudo-random codes
are produced by a local code generator 50 driven by a digitally
controlled oscillator NCO1, itself controlled by a computer 100
associated with the GPS receiver. The results of the four
multiplications are aggregated in respective accumulators 22, 24,
26, 28. The outputs Ip, Qp (correlation by punctual code P) and Id,
Qd (correlation by difference code E-L) of the accumulators are
multiplied (multipliers 31 to 38) by a value cos .PHI. and a value
sin .PHI. representing respectively the cosine and the sine of the
phase .PHI. of the carrier. The outputs from these multipliers make
it possible to compute sums and differences of products, and
periodic accumulations IpA, QpA, IdA, QdA, of these sums and
products, which represent partial results of the correlation of the
GPS signal with the code and the carrier that are generated locally
in the channel. These results are provided to the associated
computer and serve in return to drive the feedback control loop so
as to align the punctual local code P with the code present in the
satellite signal, and to align the local carrier phase with the
phase of the satellite signal.
The local carrier phase is established by a second digitally phase
controlled oscillator NCO2, which produces a sawtooth varying phase
.PHI.. This phase is applied to a sine and cosine generator to
establish the values sin .PHI., cos .PHI. from the phase .PHI.
present at the output of the local oscillator NCO2. It is this
local oscillator output, transmitted moreover to the associated
computer 100, which represents, at a measurement instant t, the
phase .PHI..sub.i(t) of the carrier in the channel corresponding to
the satellite of rank i.
The computation of hybrid position and the computation of the
protection radii will therefore be done from one measurement to the
next by observing the difference between the content of the
oscillator NCO2 at the instant t and the content at the instant t-1
and by transmitting this difference to the Kalman filter according
to what was explained above.
Having thus described the manner of operation of the Kalman filter
in relation to the carrier phase variations observed on each
satellite axis in the GPS receiver, we shall now return to the
computation of the radius of protection of the hybrid data
D.sub.--HYB. As was stated, this radius of protection is a very
important measurement in certain applications where it is essential
to ascertain the accuracy with which the data are obtained.
FIG. 4 represents a diagram for obtaining the various protection
radii computed in the hybrid inertial platform.
On the one hand the inherent radius of protection RPgps of the GPS
receiver is computed (either in the GPS receiver itself or in the
hybridization computer if the latter receives all the GPS
receiver's internal data necessary for the computation of the
protection radius: pseudo-distances PD.sub.i, signal/noise ratios
(S/N).sub.i for each satellite axis, etc.). On the other hand, a
hybrid protection radius RPH0 is computed by assuming that there is
no defective satellite in the constellation of N satellites,
observed at a given moment. Finally, a hybrid protection radius
RPH1, corresponding to the presence of a defective satellite, is
computed.
It is recalled that the radius of protection RP of a measurement,
for a predetermined probability of nondetection of error PND, is an
upper bound on the deviation between the value computed and the
actual value of the quantity measured, such that there is a
probability of less than PND that the actual value is more than a
distance RP away from the computed value. There is therefore a
maximum probability PND that the actual value is outside a circle
of radius RP around the value found by computation: maximum
probability PND that the actual error of measurement exceeds the
stated radius of protection. This amounts again to saying that
there is a maximum probability PND of being wrong in the
determination of the protection radius.
In general, the maximum probability PND is fixed as a function of
the application. In the example of the landing of an aircraft for
example, one may desire a maximum probability PND of 10.sup.-7/hour
of being wrong in the radius of protection on account of a
foreseeable or unforeseeable defect.
Now, the protection radius is related directly to the variance of
the quantity measured and to the probability of nondetection of
error PND. The variance is the square of the standard deviation
.SIGMA. related to the quantity measured. The variance of the
measured hybrid quantity is the coefficient of the diagonal of the
covariance matrix P which corresponds to the measured quantity. If
the altitude of the inertial platform is the measured quantity and
is situated in sixth place in the state vector and in the variance
matrix P, the variance of the altitude is the sixth coefficient in
the diagonal of the matrix. The standard deviation .SIGMA. is the
square root of this variance. It is therefore deduced from the
matrix P in a Kalman filter.
The protection radius RP is related to the standard deviation
.SIGMA. and the probability of nondetection PND by the following
approximate table,
TABLE-US-00001 Value of PND Value of RP 0.35/hour .SIGMA. 5
10.sup.-2/hour 2.SIGMA. 10.sup.-3/hour 3.SIGMA. 10.sup.-7/hour
5.7.SIGMA. 10.sup.-9/hour 7.SIGMA.
Depending on the probability of nondetection fixed (and hence
depending on the application envisaged), it is therefore possible
to determine a coefficient k such that the protection radius RP is
equal to k.SIGMA.. The coefficient k takes a value lying between 1
and 7 in the above table.
This protection radius is computed from the standard deviations of
the variables considered. It applies to each possible variable, but
in practice one is interested in the distance variables.
A protection radius computation is done inside the GPS receiver so
as to end up with an inherent radius of protection RPgps of the PVT
point provided by the receiver. It is even possible to compute more
specifically a vertical radius of protection for the altitude and a
horizontal radius of protection for the position in terms of
longitude and latitude, these radii not necessarily having the same
value and not being used in the same way (the vertical radius of
protection is a more critical item of data). The inherent radius of
protection of the GPS is useful for the initialization or the
reinitialization of the computation of hybridization between the
inertial platform and the GPS receiver: the initial position of the
inertial platform is assigned to be the value of the PVT point
provided by the GPS, together with its inherent radius of
protection.
Another protection radius computation is done within the
hybridization computer, in the presence of errors modeled in the
Kalman filter. More precisely two computations are done, one
assuming an absence of satellite fault, and the other assuming the
presence of a satellite fault; this leads to two hybrid radii of
protection RPH0 (absence of fault) and RPH1 (presence of fault).
The overall radius of protection will be regarded as being the
larger of the two. It is not necessary to compute a protection
radius in the case of two or more faulty satellites, the
probability of this configuration occurring being regarded as too
small.
As far as the protection radius RPH1 in the presence of a fault
with a satellite is concerned, it should firstly be noted that in
principle one knows the maximum probability of there being a defect
of the spatial segment (defect with a satellite). Let us assume
that it is 10.sup.-4/hour: this brings down the probability of
having a defect in two satellites at once to 10.sup.-8/hour, which
will be regarded here as negligible but which could be taken into
account if one wanted to further reduce the probability of
nondetection of error PND to below 10.sup.-7/hour. In what follows,
a probability of nondetection of 10.sup.-7/hour will be regarded as
a goal to be achieved whatever the configuration, fault or absence
of fault.
However, this information regarding probability of fault of the
spatial segment will be used to reduce the probability of
nondetection of a fault other than a satellite fault simultaneously
with a satellite fault.
In other words, if a satellite fault is present although such a
fault occurs only with a probability of 10.sup.-4/hour, it will be
considered that a probability of nondetection of 10.sup.-3/hour of
an error other than this fault suffices in order for a probability
of nondetection of 10.sup.-7/hour to be ensured overall. For a
probability of 10.sup.-3/hour, the ratio k of the radius of
protection to the standard deviation is only 3, whereas it is 5.7
for a probability of 10.sup.-7/hour.
In both cases, the computation of the protection radius involves
the standard deviations of the position variables considered.
Computation of the Radius of Protection RPH0 in the Absence of any
Satellite Fault
The variance of a measured quantity, for example the altitude, is
extracted from the updated covariance matrix Pa, its square root is
taken so as to obtain the standard deviation .SIGMA..sub.alt of the
same quantity, the result is multiplied by the desired ratio k=k0
(for example k0=5.7) and the hybrid protection radius RPH0 (here
for altitude: RPHO.sub.alt) is obtained in the absence of any fault
other than the errors modeled by the Kalman filter.
RPH0.sub.alt=k0..SIGMA..sub.alt
Without entering into the details, it is understood that if one
prefers an overall horizontal radius of protection rather than a
radius of protection for longitude and a radius of protection for
latitude, the variances for longitude and for latitude must be
added together to obtain an overall variance for horizontal
distance and a horizontal standard deviation.
RPH0.sub.hor=k0..SIGMA..sub.hor
The radii of protection of quantities that are distances are
obviously expressed as distances, the radii of protection of
quantities that are speeds or angles are expressed as speeds or as
angles.
This radius of protection is therefore derived directly from the
successive updates of the covariance matrix P.
Computation of the Protection Radius RPH1 in the Presence of a
Satellite Fault
As stated, if one wants an overall probability of overall
nondetection of 10.sup.-7/hour (k=k0=5.7), if the probability of a
satellite fault is 10.sup.-4/hour and if a case of satellite fault
occurs, then the probability of simultaneous nondetection of an
error in the hybridization computation process is considered to be
10.sup.-3/hour, corresponding to a coefficient k=k1=3.
The protection radius RPH1 which will be computed in this case
results from the addition of two factors: a factor k1..SIGMA.
related to the probability of nondetection of 10.sup.-3/hour for an
error modeled in the Kalman algorithms, and deviations derived from
the N+1 Kalman filtering algorithms.
It is recalled that the main filtering algorithm uses the N
satellites, and that the other N filtering algorithms exclude a
satellite of rank i on each occasion. These N secondary algorithms
each lead to a hybrid position and to associated standard
deviations for each variable (for example altitude and horizontal
distances).
Specifically, in the case when no satellite is defective, the N+1
filtering algorithms provide hybrid positions that are very close
to one another and all situated inside the protection radius RPHO
previously computed.
However, if a satellite is defective, the solutions provided by the
N+1 filtering algorithms diverge and give N+1 different error
estimates (that is to say N+1 different state vectors Xa). The
hybridization computer computes the distances between the various
solutions thus found. For example, if one is interested in the
radius of protection of the altitude, the computer can compute the
distances between the altitude solution provided by the main filter
to N+1 satellites and the altitude solution provided by each of the
N secondary filters.
Should there be a fault with a satellite, one of the secondary
filters gives an exact solution within a radius of
k1..SIGMA..sub.i, .SIGMA..sub.i being the standard deviation
computed by this secondary filter and associated with the solution
found by this filter.
All the other filters, including the main filter give a false
solution, but one does not know which secondary filter is the one
that gives the exact solution.
Hence, the distance d.sub.i between the altitude error (component
of the state vector X) given by the main filter and that which is
given by a secondary filter is computed, k1..SIGMA..sub.i is added
to this distance, .SIGMA..sub.i being the standard deviation
corresponding to this filter. This computation is done for the N
secondary filters. The maximum value out of the N values thus
computed is taken, and this value constitutes the protection radius
RPH1 in the event of a satellite fault.
RPH1altitude=SUP[(d.sub.i+k1..SIGMA..sub.i)]
The computation is similar for a horizontal radius of protection,
the standard deviation considered then being the square root of the
sum of the variances in longitude and in altitude.
Computation of the Overall Radius of Protection
Having thus computed two radii of protection RPH0 and RPH1, in the
absence and in the presence of a fault of the spatial segment, the
larger of the two values is taken to define an overall radius of
protection RPH for the hybrid solution computed by the
hybridization computer. RPH=SUP[RPH0, RPH1]
This protection radius is computed as a vertical distance on the
one hand, and as a horizontal distance on the other hand.
This hybridization between a single inertial platform and a GPS
receiver does not allow account to be taken of any unmodeled fault
with the inertial platform or with the GPS receiver (for example a
GPS fault affecting all the channels of the receiver).
It will be readily seen by one of ordinary skill in the art that
the present invention fulfills all of the objects set forth above.
After reading the foregoing specification, one of ordinary skill
will be able to affect various changes, substitutions of
equivalents and various other aspects of the invention as broadly
disclosed herein. It is therefore intended that the protection
granted hereon be limited only by the definition contained in the
appended claims and equivalents thereof.
If one wants to take such faults into account, a redundancy must be
introduced, with a second inertial platform, a second GPS receiver
and a second hybridization computer. The first hybridization chain
provides a first hybrid solution which will be considered to be the
main solution, with an associated standard deviation .SIGMA.; the
second chain provides a hybrid solution with an associated standard
deviation. If the probability of a hardware fault is considered to
be 10.sup.-4/hour, then a radius of protection of 3.SIGMA. around
each hybrid solution is sufficient. The distance between the two
hybrid solutions is computed, one being right within a radius of
3.SIGMA. and the other being false, the larger of the two 3.SIGMA.
values being added to this distance; the sum thus computed
constitutes an overall radius of protection of the main hybrid
solution in the presence of a fault with one or the other of the
chains: the exact solution lies inside a circle having this radius,
around the main hybrid solution, with an error probability of
10.sup.-3/hour in this example.
Given that the main hybrid solution itself has an associated radius
of protection, in the absence of a fault, which is 5.7.SIGMA. for
the desired overall probability of 10.sup.-7/hour, one determines
which is the higher radius of protection out of the latter and the
overall radius of protection in the presence of a fault with one or
the other of the chains. The higher of the two values constitutes,
for the hybridized platform with two hybridization chains, the
overall radius of protection around the hybrid solution of the main
chain. It is this overall radius of protection that is provided to
the user.
It will be noted that it is not possible to determine which of the
two chains is defective if there is no third pathway. This is why
the user is given a single hybrid solution which is that of the
chain considered by assumption to be the main chain (each of the
two chains may be considered as the main one if the chains are
identical).
The explanations just provided show that the protection radius thus
computed varies gradually: there is no abrupt jump, either in the
case of a single hybridization chain or in the case of redundancy
with two chains.
The inherent radius of protection of the GPS may be used to reset
the hybrid data: when the inherent radius of protection of the GPS
becomes less than the overall radius of protection of the hybrid
platform, the position data of the GPS may be provided as output
data from the hybrid platform.
Returning now to the case of a spatial segment fault, caused by a
defective satellite, it is desirable to be able to ascertain the
identity of the defective satellite, and to exclude this satellite
from the subsequent measurements. In the case of two hybridization
chains, it will be verified that it is the same satellite that is
identified as being defective before excluding it.
To perform this exclusion, it is best to consider the innovations
(INNOV) of the Kalman filters as gaussian variables in the absence
of any fault; the sum of the squares of the innovations of each of
the filters is computed periodically, and is normalized by the
associated standard deviations which may vary from one filter to
another. A Khi2 law is applied to these sums. No inconsistency
should be seen to appear. If an inconsistency appears, it appears
in principle on all the filters except the one which does not use
the defective satellite. It can thus be identified, excluded from
the subsequent computations, and the hybrid data can immediately be
reset to the data provided by the secondary Kalman filter which
does not include the defective satellite. The inconsistency is
determined on the basis of a threshold which depends on the false
alarm probability and the nondetection probability fixed.
The invention is applicable in the case of the use of DGPS
receivers, that is to say of receiver receiving, in addition to the
satellite signals, correction signals sent by local ground stations
which receive the same signals from satellites and whose exact
position is known. The ground station sends corrections of
pseudo-distances and it is the pseudo-distances PD.sub.i thus
corrected which serve for the initialization of the hybridization,
the Kalman filter then being fed with carrier phase variations as
has been explained.
* * * * *